Specific impulse

The specific momentum of a rocket engine is the change in momentum per ejected mass (combustion gases or supporting mass ). The specific impulse - it is the effective exit speed - is an essential parameter of a drive or a fuel regardless of the size of the engine. ${\displaystyle I_{\mathrm {sp} }}$

The unit of specific impulse is meters per second (m / s), the same as that of speed . In the case of rocket engines, it is common to describe the mass as its weight under normal fall acceleration , whereby the (weight) specific impulse is shown in the unit s. A specific impulse given in this unit can be converted into the SI-compliant value by multiplying it by the gravitational acceleration of around 9.806 m / s ² .

definition

The specific impulse is

${\displaystyle I_{\mathrm {sp} }={\frac {\mathrm {d} p}{\mathrm {d} m}}={\frac {\dot {p}}{\dot {m}}}={\frac {F}{\dot {m}}}}$

with the momentum and the ejected mass The dots stand for , the time derivative. so is the mass throughput . The resulting rate of change of momentum , the force , is called thrust . Since the momentum has the dimension mass times velocity and the mass cancels out, the SI-conform unit is m / s, imperial ft / s. ${\displaystyle p}$ ${\displaystyle m.}$ ${\displaystyle {\tfrac {\mathrm {d} }{\mathrm {d} t}}}$ ${\displaystyle {\dot {m}}}$ ${\displaystyle {\dot {p}}}$ ${\displaystyle F}$ ${\displaystyle I_{\mathrm {sp} }}$

By dividing the specific impulse with the standard acceleration due to gravity , one obtains a physical quantity of the quantity type time ( ). ${\displaystyle g_{0}}$ ${\displaystyle I_{\mathrm {sp} }/g_{0}}$

Example values ​​for engines

The specific impulse of a chemical rocket engine is determined by the exit speed (determined by the enthalpy of reaction and the density of the fuel, the temperature increase or reaction speed achieved, the design and the completeness of the combustion). The highest specific impulses in the fuel combinations used today are achieved with hydrogen + oxygen and hydrogen + fluorine. The highest experimentally achieved value is around 4600 m / s ( RL-10B2 and Vinci engine ).

Ion thrusters use electric fields to accelerate ions. A working medium is ionized for this purpose. Depending on the voltage applied, the ions can be accelerated to very high speeds, theoretically up to almost the speed of light. Available ion thrusters have specific impulses of 30 to 40 km / s, the dual-stage 4-grid ion drive (DS4G) from ESA achieved a specific impulse of 210 km / s.

application

The specific momentum of a rocket engine depends on the ambient pressure. The construction of the Laval nozzle is optimized for a specific final pressure. Upper grades develop the highest specific impulse in a vacuum. When starting from earth, the maximum achievable specific impulse is 10 to 15 percent lower because of the atmospheric pressure, since one cannot expand below about 40 percent of the external pressure at lower stages. Otherwise, the normally used bell jets will break the flow ( Summerfield criterion ). An alternative that works equally efficiently in both air and vacuum is the aerospike engine.

Since the mass-specific impulse represents the effective outflow velocity of the gases in SI units, the final velocity of the rocket can be calculated from Ziolkowski's basic rocket equation together with the full and empty mass .

The volume-specific impulse is also important for rockets that are used within the atmosphere, as well as for military rockets that have to be housed in a silo or in a transport container that is as small as possible , because one then wants to build as compact as possible, i.e. with low air resistance. It is formed by multiplying the specific impulse by the density of the fuel : ${\displaystyle V_{\mathrm {Isp} }}$ ${\displaystyle \rho }$

${\displaystyle V_{\mathrm {Isp} }=\rho I_{\mathrm {sp} }}$

For example, the specific impulse of the combination of nitrogen tetroxide with hydrazine variants is somewhat smaller than that of liquid oxygen and kerosene . However, the density is higher, and so you get a smaller missile.

Web links

• Propulsion Dual-stage Gridded Ion Thruster (DS4G) ( Memento from February 27, 2014 in the Internet Archive )
• RL-10 Characteristics (Rocketdyne) ( Memento from February 10, 2010 in the Internet Archive )
• Specific impulses . NASA Glenn Research Center

Individual evidence

1. ↑ Emma Young: Super-powerful new ion engine revealed. New Scientist, January 18, 2006, accessed November 18, 2013 .